Finite Group Databasebeta

← #18077783

Subgroups — #18077783

Order 4864.

432 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572584C211yesmaximal, characteristic
2#14564580C211yesmaximal, characteristic
3#14562134C211yesmaximal, characteristic
4#14562038C211yesmaximal, characteristic
5#14561475C211yesmaximal, characteristic
6#14561472C211yesmaximal, characteristic
7C19×#3170C211yesmaximal, characteristic
8#11926675—21no—
9#11926675—22no—
10Q8×C19⋊C8—21no—
11#11926597C2211yescharacteristic
12#11926571—21no—
13C2×C4⋊(C19⋊C8)C2211yescharacteristic
14#11926500—21no—
15C4×#64520C2211yescharacteristic
16C4×C4⋊Dic19C2211yescharacteristic
17#11926303—21no—
18#11926303—21no—
19#11926281—22no—
20Q8⋊(C19⋊C8)—21no—
21Q8⋊(C19⋊C8)—21no—
22C19×#533C2211yescharacteristic
23C19×#533C2211yescharacteristic
24C19×#500C411yescharacteristic, complemented
25C19×#494C411yescharacteristic, complemented
26C19×#487C411yescharacteristic, complemented
27C19×#487C411yescharacteristic, complemented
28C19×#467—22no—
29C4×Q16×C19—22no—
30C2×C4×C8×C19C2211yescharacteristic
31C2×Q16×C19—22no—
32C22×C8×C19—21no—
33C19×C4⋊Q8C2×C411yescharacteristic
34C19×C4⋊Q8C2×C411yescharacteristic
35C19×C4⋊Q8C2×C411yescharacteristic
36C19×C4⋊Q8C2×C411yescharacteristic
37C19×#125—21no—
38C19×#125—21no—
39C19×C22⋊Q8—21no—
40C19×C22⋊Q8—21no—
41C19×C22⋊Q8—21no—
42C19×C22⋊Q8D412yes—
43C4×Q8×C19—21no—
44C4×Q8×C19—21no—
45C4×Q8×C19—21no—
46C4×Q8×C19D412yes—
47C19×#117—21no—
48C19×#117—21no—
49C2×C42×C19C2311yescharacteristic
50C2×C4⋊Dic19—21no—
51C2×C4×Dic19—21no—
52C2×#64520D411yescharacteristic
53C2×#64520D411yescharacteristic
54C22×C19⋊C8—21no—
55C19×#107—22no—
56C19×#103—22no—
57C19×#103—22no—
58C4×C8×C19—21no—
59C4×C8×C19C2×C411yescharacteristic
60C4×C8×C19C2×C411yescharacteristic
61C19⋊#95—21no—
62C22⋊(C19⋊C8)—21no—
63C4⋊(C19⋊C8)—22no—
64C4⋊(C19⋊C8)—22no—
65C4⋊(C19⋊C8)—21no—
66C4⋊(C19⋊C8)—21no—
67C4⋊(C19⋊C8)D411yescharacteristic
68C4⋊(C19⋊C8)D411yescharacteristic
69#10597260—22no—
70#10597260—21no—
71C4×C19⋊C8—22no—
72C4×C19⋊C8—21no—
73C4×C19⋊C8—21no—
74C2×Q8×C19—21no—
75C2×Q8×C19—21no—
76C2×Q8×C19—21no—
77C2×Q8×C19C22⋊C412yes—
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19#4111yescharacteristic
81C22×Dic19—41no—
82Q16×C19—44no—
83C2×C8×C19—21no—
84C2×C8×C19—21no—
85C2×C8×C19—42no—
86C4⋊C4×C19—21no—
87C4⋊C4×C19—21no—
88C4⋊C4×C19—21no—
89C4⋊C4×C19—22no—
90C4⋊C4×C19—22no—
91C4⋊C4×C19—21no—
92C4⋊C4×C19—21no—
93C4⋊C4×C19—21no—
94C4⋊C4×C19—21no—
95C4⋊C4×C19—41no—
96C4⋊C4×C19—41no—
97C4⋊C4×C19C22⋊C412yes—
98C22⋊C4×C19—22no—
99C22⋊C4×C19—41no—
100C42×C19—22no—
101C42×C19—41no—
102C42×C19C22×C411yescharacteristic
103C42×C19C2×D411yescharacteristic
104C42×C19C2×D411yescharacteristic
105C42×C19#4111yescharacteristic
106C4⋊Dic19—22no—
107C4⋊Dic19—41no—
108C4×Dic19—41no—
109C4×Dic19—41no—
110#64520—21no—
111#64520—21no—
112#64520—21no—
113#64520Q1612yescomplemented
114C2×C19⋊C8—21no—
115C2×C19⋊C8—21no—
116C2×C19⋊C8—21no—
117C2×C19⋊C8—21no—
118C2×C19⋊C8—41no—
119C2×C19⋊C8—41no—
120C2×C19⋊C8—41no—
121#9056—191nomaximal, Sylow
122C23×C19#12111yescharacteristic
123Q8×C19—42no—
124Q8×C19—42no—
125Q8×C19—41no—
126Q8×C19—41no—
127Q8×C19—41no—
128Q8×C19—41no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—22no—
132C2×C4×C19—22no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19—41no—
136C2×C4×C19C2×C22⋊C411yescharacteristic
137C2×C4×C19C4×D411yescharacteristic
138C2×C4×C19C4×D411yescharacteristic
139C2×C4×C19#12011yescharacteristic
140C2×C4×C19#12111yescharacteristic
141C2×C4×C19#12311yescharacteristic
142C2×C4×C19C2×Q1611yescharacteristic
143C2×C4×C19#13511yescharacteristic
144C2×C4×C19#13711yescharacteristic
145C2×C4×C19#13711yescharacteristic
146C2×Dic19—42no—
147C2×Dic19—81no—
148C2×Dic19—81no—
149C8×C19—22no—
150C8×C19—41no—
151C19⋊C8—22no—
152C19⋊C8—41no—
153C19⋊C8—41no—
154C19⋊C8—41no—
155C19⋊C8—81no—
156#3170D1911yescharacteristic
157#2962—191no—
158#1986—191no—
159#1503—191no—
160#1481—191no—
161#1279—191no—
162#1278—191no—
163C22×C19—21no—
164C22×C19—21no—
165C22×C19#38611yescharacteristic
166C22×C19#46211yescharacteristic
167C22×C19#46411yescharacteristic
168C4×C19—21no—
169C4×C19—21no—
170C4×C19—21no—
171C4×C19—42no—
172C4×C19—42no—
173C4×C19—81no—
174C4×C19—81no—
175C4×C19C4×Q1611yescharacteristic
176C4×C19#44111yescharacteristic
177C4×C19#44311yescharacteristic
178C4×C19#44411yescharacteristic
179C4×C19#45111yescharacteristic
180C4×C19#45211yescharacteristic
181Dic19—82no—
182#533C2×D1911yescharacteristic
183#533C2×D1911yescharacteristic
184#500Dic1911yescharacteristic, complemented
185#494Dic1911yescharacteristic, complemented
186#487Dic1911yescharacteristic, complemented
187#487Dic1911yescharacteristic, complemented
188#467—22no—
189#446—381no—
190#446—382no—
191C8×Q8—381no—
192C4×Q16—22no—
193#431—191no—
194#424—381no—
195C2×C4⋊C8—191no—
196#405—381no—
197C4×M16—191no—
198C2×C4×C8C2×D1911yescharacteristic
199C4×C4⋊C4—191no—
200#339—381no—
201#339—381no—
202#328—382no—
203Q8⋊C8—381no—
204Q8⋊C8—381no—
205C2×C19—21no—
206C2×C19—21no—
207C2×C19#187611yescharacteristic
208C2×C19#187811yescharacteristic
209C2×C19#188411yescharacteristic
210C2×Q16—22no—
211C2×M16—191no—
212C2×M16—191no—
213C22×C8—21no—
214C22×C8—381no—
215C4⋊Q8C2×Dic1911yescharacteristic
216C4⋊Q8C2×Dic1911yescharacteristic
217C4⋊Q8C2×Dic1911yescharacteristic
218C4⋊Q8C2×Dic1911yescharacteristic
219#125—21no—
220#125—21no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C22⋊Q8—21no—
224C22⋊Q8C22⋊D1912yes—
225C4×Q8—21no—
226C4×Q8—21no—
227C4×Q8—21no—
228C4×Q8C22⋊D1912yes—
229#117—21no—
230#117—21no—
231C2×C4⋊C4—381no—
232C2×C42—381no—
233C2×C42C22×D1911yescharacteristic
234#107—22no—
235C4⋊C8—191no—
236C4⋊C8—191no—
237C4⋊C8—382no—
238C4⋊C8—382no—
239C4⋊C8—381no—
240C4⋊C8—381no—
241#103—22no—
242#103—22no—
243C22⋊C8—381no—
244#97—382no—
245#97—381no—
246C4×C8—21no—
247C4×C8—382no—
248C4×C8—381no—
249C4×C8—381no—
250C4×C8C2×Dic1911yescharacteristic
251C4×C8C2×Dic1911yescharacteristic
252#95—381no—
253C19#905611yescharacteristic, complemented, Sylow
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8C22⋊Dic1912yes—
258C22×C4—761no—
259C22×C4D4×D1911yescharacteristic
260C22×C4#6454311yescharacteristic
261C22×C4C2×C22⋊D1911yescharacteristic
262Q16—44no—
263M16—192no—
264M16—381no—
265M16—381no—
266M16—381no—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—42no—
270C2×C8—381no—
271C2×C8—381no—
272C2×C8—381no—
273C2×C8—381no—
274C2×C8—761no—
275C2×C8—761no—
276C2×C8—761no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—382no—
289C4⋊C4—761no—
290C4⋊C4C22⋊Dic1912yes—
291C22⋊C4—22no—
292C22⋊C4—41no—
293C42—22no—
294C42—41no—
295C42—761no—
296C42—761no—
297C42D4×D1911yescharacteristic
298C42#6454311yescharacteristic
299C42C22×Dic1911yescharacteristic
300C42C2×C22⋊D1911yescharacteristic
301C23#1059738511yescharacteristic
302Q8—42no—
303Q8—42no—
304Q8—41no—
305Q8—41no—
306Q8—41no—
307Q8—41no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—762no—
316C2×C4—1521no—
317C2×C4—1521no—
318C2×C4Q16×D1911yescharacteristic
319C2×C4#1059736411yescharacteristic
320C2×C4#1059736411yescharacteristic
321C2×C4#1059736511yescharacteristic
322C2×C4D4×Dic1911yescharacteristic
323C2×C4D4×Dic1911yescharacteristic
324C2×C4#1059738111yescharacteristic
325C2×C4#1059738311yescharacteristic
326C2×C4#1059738511yescharacteristic
327C2×C4C2×C22⋊Dic1911yescharacteristic
328C8—22no—
329C8—41no—
330C8—382no—
331C8—761no—
332C8—761no—
333C8—761no—
334C8—1521no—
335C22—21no—
336C22—21no—
337C22#1192642411yescharacteristic
338C22#1192675211yescharacteristic
339C22#1192676811yescharacteristic
340C4—21no—
341C4—21no—
342C4—21no—
343C4—42no—
344C4—42no—
345C4—81no—
346C4—81no—
347C4—1522no—
348C4Q16×Dic1911yescharacteristic
349C4#1192665111yescharacteristic
350C4#1192666111yescharacteristic
351C4#1192666611yescharacteristic
352C4#1192669811yescharacteristic
353C4#1192670511yescharacteristic
354C2—21no—
355C2—21no—
356C2#1456396411yescharacteristic
357C2#1456397811yescharacteristic
358C2#1456401911yescharacteristic
subgroupG/H
centerC2×C4#10597383
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#3170C2
socleC22×C19#386
prime radicalC23×C19#121
cosocleC2×C42×C19C23
hypercenter#3170D19
hypocenterC19#9056
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3170

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
24. C19×#500C4semidirect
25. C19×#494C4semidirect
26. C19×#487C4semidirect
27. C19×#487C4semidirect
113. #64520Q16semidirect
184. #500Dic19semidirect
185. #494Dic19semidirect
186. #487Dic19semidirect
187. #487Dic19semidirect
253. C19#9056semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145725842
#145645802
#145621342
#145620382
#145614752
#145614722
C19×#31702
#905619